DOCSLIB.ORG

Planar Josephson Hall Effect in Topological Josephson Junctions

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Planar Josephson Hall Effect in Topological Josephson Junctions PHYSICAL REVIEW B 103, 054508 (2021) Planar Josephson Hall effect in topological Josephson junctions Oleksii Maistrenko ,1,* Benedikt Scharf ,2 Dirk Manske,1 and Ewelina M. Hankiewicz2,† 1Max-Planck-Institut für Festkörperforschung, D-70569 Stuttgart, Germany 2Institute for Theoretical Physics and Astrophysics and Würzburg-Dresden Cluster of Excellence ct.qmat, University of Würzburg, Am Hubland, 97074 Würzburg, Germany (Received 11 March 2020; revised 1 February 2021; accepted 2 February 2021; published 17 February 2021) Josephson junctions based on three-dimensional topological insulators offer intriguing possibilities to realize unconventional p-wave pairing and Majorana modes. Here, we provide a detailed study of the effect of a uniform magnetization in the normal region: We show how the interplay between the spin-momentum locking of the topological insulator and an in-plane magnetization parallel to the direction of phase bias leads to an asymmetry of the Andreev spectrum with respect to transverse momenta. If sufficiently large, this asymmetry induces a transition from a regime of gapless, counterpropagating Majorana modes to a regime with unprotected modes that are unidirectional at small transverse momenta. Intriguingly, the magnetization-induced asymmetry of the Andreev spectrum also gives rise to a Josephson Hall effect, that is, the appearance of a transverse Josephson current. The amplitude and current phase relation of the Josephson Hall current are studied in detail. In particular, we show how magnetic control and gating of the normal region can enable sizable Josephson Hall currents compared to the longitudinal Josephson current. Finally, we also propose in-plane magnetic fields as an alternative to the magnetization in the normal region and discuss how the planar Josephson Hall effect could be observed in experiments. DOI: 10.1103/PhysRevB.103.054508 I. INTRODUCTION Topological Josephson junctions are particularly intrigu- ing if they are based on 3D TIs, as depicted in Fig. 1(a): The helical spin structure of the surface states of three- Because of the 2D nature of the surface, the system sup- dimensional topological insulators (3D TIs) offers intriguing ports modes that propagate along the direction parallel to the possibilities of tailoring the surface-state properties by vari- superconductor/normal TI interface, that is, the y direction ous proximity effects. A conventional s-wave superconductor in Fig. 1(a). Due to the protected zero-energy crossing oc- can, for example, be used to proximity-induce superconduc- curring at zero transverse momentum and phase difference tivity in the TI surface. The interplay between the helical φ = π,aπ junction exhibits two counterpropagating gapless spin-momentum locking of the TI surface state and the super- states, so-called nonchiral Majorana modes [1][seeFig.1(b) conducting pairing then mediates an effective pairing between bottom]. electrons at the Fermi level. This effective pairing features a Besides proximity-induced superconductivity, one can also mixture of singlet s-wave and triplet p-wave pair correlations envision other proximity effects whose interplay with the [1–3] and turns the TI surface into a topological superconduc- spin texture of the TI surface state leads to novel phenom- tor [2,4–9] with Majorana zero modes [1] and odd-frequency ena: In nonsuperconducting setups, for example, the interplay pairing [10]. between the helical surface states and proximity-induced mag- In this context, Josephson junctions based on 3D TIs or netism provides a versatile platform for studying fundamental on their two-dimensional (2D) counterparts have been studied effects and spintronic applications [4,32,33]. Ferromagnetic extensively for potential signatures of topological supercon- tunnel junctions based on 3D TIs [34–38], in particular, ductivity, both theoretically [1,3,11–24] and experimentally show some promise for potential spintronic devices [39]. The [25–29]. These so-called topological Josephson junctions ex- combination of 3D TIs with both proximity-induced super- hibit a ground-state fermion parity that is 4π-periodic in the conductivity and magnetism can prove even more interesting superconducting phase difference φ and Andreev bound states [11,40–42], however, and could point to novel possibilities for (ABS) with a protected zero-energy crossing [30,31]. superconducting spintronics [43,44]. Motivated by this prospect [45] as well as by phenomena found in nonsuperconducting TI tunneling junctions, such as *Corresponding author: [email protected] the tunneling planar Hall effect [38], we study 3D TI-based †Corresponding author: [email protected] Josephson junctions with a ferromagnetic tunneling barrier Published by the American Physical Society under the terms of the [see Fig. 1(c)]. In contrast to previous studies on this system Creative Commons Attribution 4.0 International license. Further [11,40,41], we focus not only on the longitudinal response distribution of this work must maintain attribution to the author(s) but also on the transverse response to an applied phase bias. and the published article’s title, journal citation, and DOI. Open We find that especially the configuration with an in-plane access publication funded by the Max Planck Society. magnetization parallel to the direction of the phase bias 2469-9950/2021/103(5)/054508(16) 054508-1 Published by the American Physical Society OLEKSII MAISTRENKO et al. PHYSICAL REVIEW B 103, 054508 (2021) II. MODEL A. Hamiltonian and unitary transformation In our model, we consider a Josephson junction based on the 2D surface state of a 3D TI, as depicted in Fig. 1(c), where the pairing in the superconducting (S) regions is induced from a nearby s-wave superconductor. The ferromagnetic (F) region is subject to an exchange splitting/Zeeman term proximity induced from a nearby ferromagnet [48]. If one is only inter- ested in an in-plane Zeeman term, an alternative way to realize such a Zeeman term is by applying an in-plane magnetic field as discussed in Sec. VII below. The surface state lies in the xy plane, with the direction of the superconducting phase bias denoted as the x direction. We take the system to be infinite in both the x and y directions. Here, we study the regime FIG. 1. (a) Scheme of a Josephson junction based on a 3D TI: where the Fermi level is situated inside the bulk gap and s-wave superconductors (S) on top of the TI proximity-induced where only surface states exist. Moreover, we assume that pairing into the TI surface state. The two proximity-induced super- the surface considered is far enough away from the opposite conducting regions are separated by a normal region. (b) Top view surface so that there is no overlap between their states. Then, and low-energy Andreev spectrum of a short topological π junction the Josephson junction based on a single surface is described for transverse momenta py close to py = 0: The two low-energy by the Bogoliubov-de Gennes (BdG) Hamiltonian ABS correspond to counterpropagating nonchiral Majorana modes with opposite group velocities. No net Josephson Hall current flows 0 Hˆ = [vF (σx pˆy − σy pˆx ) − μ]τz + (V0τz − M · σ)h(x) in the y direction. (c) Ferromagnetic Josephson junction based on BdG a 3D TI: Same as (a) but with a magnetic region separating the + (x)[τx cos (x) − τy sin (x)] (1) superconducting regions. In this setup, the Zeeman field/exchange splitting M is proximity induced by a ferromagnet (F). (d) Same † † T with the basis order ˆ = (ψˆ↑, ψˆ↓, ψˆ , −ψˆ ) .InEq.(1), as (a) but for a ferromagnetic Josephson junction with large M ↓ ↑ pˆl (with l = x, y) denote momentum operators and σl and parallel to the direction of the phase bias: The Andreev spectrum is τ = , , asymmetric and has been tilted in such a way that the two low-energy l (with l x y z) Pauli matrices in spin and particle-hole space, respectively. Moreover, σ = (σx,σy,σz ) and unit ma- modes are unidirectional for small py. Note that these ABS are no Majorana modes protected against backscattering because there are trices are not written explicitly in Eq. (1). In this paper, we study two models for a Josephson junc- additional zero-energy states for py close to the Fermi momentum (not shown). The asymmetry in the Andreev spectrum gives rise to a tionwithaFregionofwidthd: (a) a model with a δ-like finite Josephson Hall current flowing in the y direction. F region described by h(x) = dδ(x) and (x) = and (b) a model with a finite F region where h(x) = (d/2 −|x|) and (x) = (|x|−d/2). In both cases, the phase conven- tion is (x) = φ (x), where φ is the superconducting phase exhibits striking features: Such a magnetization leads to an difference between the two S regions. The superconducting asymmetric Andreev spectrum for a fixed finite transverse pairing amplitude with strength 0 is proximity induced momentum. If sufficiently large, this asymmetry even induces from the s-wave superconductors deposited on the TI surface. a transition from the regime of counterpropagating, nonchiral The density of states of these superconductors is typically Majorana modes to a regime with unprotected unidirectional much larger than that of the TI surface states, e.g., we can modes at small transverse momenta [compare Fig. 1(b) bot- assume Nb superconductors used in experiments. Therefore, tom and Fig. 1(d) bottom]. Most importantly, even a small the currents flowing in the TI surface do not significantly magnetization-induced asymmetry in the Andreev spectrum affect the superconducting phases and we can use constant φ causes a transverse Josephson Hall current [see Fig. 1(d) top]. and within each superconducting lead. In other words the In contrast to other Josephson Hall effects [46,47], the effect resistivity of the junction region is much larger than that of found here arises from an in-plane magnetization, which is the leads; this justifies our approximation [49,50] commonly why we call it the planar Josephson Hall effect.
Load more

Recommended publications
  • Application of the Josephson Effect to Voltage Metrology
    Application of the Josephson Effect to Voltage Metrology SAMUEL P. BENZ, SENIOR MEMBER, IEEE, AND CLARK A. HAMILTON, FELLOW, IEEE Invited Paper The unique ability of a Josephson junction to control the flow of worldwide set of units that is uniform and coherent. The am- magnetic flux quanta leads to a perfect relationship between fre- pere is the only electrical unit belonging to the seven base quency and voltage. Over the last 30 years, metrology laboratories units of the SI. The ampere is defined as “that constant cur- have used this effect to greatly improve the accuracy of dc voltage standards. More recent research is focused on combining the ideas rent which, if maintained in two parallel straight conduc- of digital signal processing with quantum voltage pulses to achieve tors of infinite length, of negligible circular cross section, similar gains in ac voltage metrology. The integrated circuits that and placed 1 meter apart in vacuum, would produce between implement these ideas are the only complex superconducting elec- these conductors a force equal to 2 10 newtons per meter tronic devices that have found wide commercial application. of length.” Keywords—Digital–analog conversion, Josephson arrays, quan- The volt, which is not a base unit, is defined through tization, standards. coherency of electrical power (current times voltage) and mechanical power (force times distance divided by time): I. INTRODUCTION “The volt is that electromotive force between two points on a conductor carrying a constant current of 1 ampere when In 1962, B. Josephson, a graduate student at Cambridge the power dissipated between the two points is 1 watt.” University, Cambridge, U.K., derived equations for the cur- Realization of the SI volt, therefore, depends on experiments rent and voltage across a junction consisting of two super- that relate the ampere and the volt to the mechanical units of conductors separated by a thin insulating barrier [1].
    [Show full text]
  • Monte Carlo Simulation Study of 1D Josephson Junction Arrays
    Monte Carlo Simulation Study of 1D Josephson Junction Arrays OLIVER NIKOLIC Master Thesis Stockholm, Sweden 2016 Typeset in LATEX TRITA-FYS 2016:78 ISSN 0280-316X ISRN KTH/FYS/-16:78-SE Scientific thesis for the degree of Master of Engineering in the subject of theoretical physics. © Oliver Nikolic, December 2016 Printed in Sweden by Universitetsservice US AB iii Abstract The focus in this thesis is on small scale 1D Josephson junction arrays in the quantum regime where the charging energy is comparable to the Joseph- son energy. Starting from the general Bose-Hubbard model for interacting Cooper pairs on a 1D lattice the problem is mapped through a path integral transformation to a classical statistical mechanical (1+1)D model of diver- gence free space-time currents which is suitable for numerical simulations. This model is studied using periodic boundary conditions, in the absence of external current sources and in a statistical canonical ensemble. It is explained how Monte Carlo simulations of this model can be constructed based on the worm algorithm with efficiency comparable to the best cluster algorithms. A description of how the effective energy Ek, voltage Vk and inverse capacitance −1 Ck associated with an externally imposed charge displacement k can be ex- tracted from simulations is presented. Furthermore, the effect of inducing charge by connecting an external voltage source to one island in the chain via the ground capacitance is investigated. Simulation results display periodic −1 response functions Ek, Vk and Ck as the charge displacement is varied. The shape of these functions are largely influenced by the system parameters and evolves from sinusoidal with exponentially small amplitude deep inside the superconducting regime towards more intriguing shapes closer to the insulat- ing regime where interactions among quantum phase slips are present.
    [Show full text]
  • Transition from Phase Slips to the Josephson Effect in a Superfluid 4He Weak Link
    1 Transition from phase slips to the Josephson effect in a superfluid 4He weak link E. Hoskinson1, Y. Sato1, I. Hahn2 and R. E. Packard1 1Department of Physics, University of California, Berkeley, CA, 94720, USA. 2Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA The rich dynamics of flow between two weakly coupled macroscopic quantum reservoirs has led to a range of important technologies. Practical development has so far been limited to superconducting systems, for which the basic building block is the so-called superconducting Josephson weak link1. With the recent observation of quantum oscillations2 in superfluid 4He near 2K, we can now envision analogous practical superfluid helium devices. The characteristic function which determines the dynamics of such systems is the current-phase relation I s (ϕ) , which gives the relationship between the superfluid current I s flowing through a weak link and the quantum phase difference ϕ across it. Here we report the measurement of the current-phase relation of a superfluid 4He weak link formed by an array of nano- apertures separating two reservoirs of superfluid 4He. As we vary the coupling strength between the two reservoirs, we observe a transition from a strongly coupled regime in which I s (ϕ) is linear and flow is limited by 2π phase slips, to a weak coupling regime where I s (ϕ) becomes the sinusoidal signature of a Josephson weak link. The dynamics of flow between two weakly coupled macroscopic quantum reservoirs can be highly counterintuitive. In both superconductors and superfluids, 2 currents will oscillate through a constriction (weak link) between two reservoirs in response to a static driving force which, in a classical system, would simply yield flow in one direction.
    [Show full text]
  • Josephson Tunneling at the Atomic Scale: the Josephson EEct As a Local Probe
    Josephson Tunneling at the Atomic Scale: The Josephson Eect as a Local Probe THIS IS A TEMPORARY TITLE PAGE It will be replaced for the nal print by a version provided by the service academique. Thèse n. 6750 2015 présentée le 22 juillet 2015 à la Faculté des Sciences des Bases Laboratoire á l'Echelle Nanométrique Programme Doctoral en Physique École Polytechnique Fédérale de Lausanne pour l'obtention du grade de Docteur des Sciences par Berthold Jäck acceptée sur proposition du jury: Prof. Andreas Pautz, président du jury Prof. Klaus Kern, directeur de thèse Prof. Davor Pavuna, rapporteur Prof. Hermann Suderow, rapporteur Dr. Fabien Portier, rapporteur Lausanne, EPFL, 2015 Non est ad astra mollis e terris via — Lucius Annaeus Seneca Acknowledgements It took me about three and a half years, with many ups and downs, to complete this thesis. At this point, I want to say thank you to all the people that supported me on my way by any means. First of all, I am grateful to Prof. Klaus Kern for giving me the opportunity to perform my doctoral studies under his supervision at the Max-Planck-Institute for Solid State Research in Stuttgart, Germany. For the entire time of my studies, I enjoyed a significant scientific freedom, such that I had the great possibility to pursue and realize my own ideas. In particular, I want to acknowledge his personal support, which allowed me to attend conferences, workshops and schools, have interesting scientific discussions as well as a wonderful time in the whole of Europe and across the USA.
    [Show full text]
  • Surprising New States of Matter Called Time Crystals Show the Same Symmetry Properties in Time That Ordinary Crystals Do in Space by Frank Wilczek
    PHYSICS CRYSTAL S IN TIME Surprising new states of matter called time crystals show the same symmetry properties in time that ordinary crystals do in space By Frank Wilczek Illustration by Mark Ross Studio 28 Scientific American, November 2019 © 2019 Scientific American November 2019, ScientificAmerican.com 29 © 2019 Scientific American Frank Wilczek is a theoretical physicist at the Massachusetts Institute of Technology. He won the 2004 Nobel Prize in Physics for his work on the theory of the strong force, and in 2012 he proposed the concept of time crystals. CRYSTAL S are nature’s most orderly suBstances. InsIde them, atoms and molecules are arranged in regular, repeating structures, giving rise to solids that are stable and rigid—and often beautiful to behold. People have found crystals fascinating and attractive since before the dawn of modern science, often prizing them as jewels. In the 19th century scientists’ quest to classify forms of crystals and understand their effect on light catalyzed important progress in mathematics and physics. Then, in the 20th century, study of the fundamental quantum mechanics of elec- trons in crystals led directly to modern semiconductor electronics and eventually to smart- phones and the Internet. The next step in our understanding of crystals is oc- These examples show that the mathematical concept IN BRIEF curring now, thanks to a principle that arose from Al- of symmetry captures an essential aspect of its com- bert Einstein’s relativity theory: space and time are in- mon meaning while adding the virtue of precision. Crystals are orderly timately connected and ultimately on the same footing.
    [Show full text]
  • Eltsov, VB AC Josephson Effect Between Two
    This is an electronic reprint of the original article. This reprint may differ from the original in pagination and typographic detail. Autti, S.; Heikkinen, P. J.; Mäkinen, J. T.; Volovik, G. E.; Zavjalov, V. V.; Eltsov, V. B. AC Josephson effect between two superfluid time crystals Published in: Nature Materials DOI: 10.1038/s41563-020-0780-y Published: 01/02/2021 Document Version Peer reviewed version Please cite the original version: Autti, S., Heikkinen, P. J., Mäkinen, J. T., Volovik, G. E., Zavjalov, V. V., & Eltsov, V. B. (2021). AC Josephson effect between two superfluid time crystals. Nature Materials, 20(2), 171-174. https://doi.org/10.1038/s41563- 020-0780-y This material is protected by copyright and other intellectual property rights, and duplication or sale of all or part of any of the repository collections is not permitted, except that material may be duplicated by you for your research use or educational purposes in electronic or print form. You must obtain permission for any other use. Electronic or print copies may not be offered, whether for sale or otherwise to anyone who is not an authorised user. Powered by TCPDF (www.tcpdf.org) AC Josephson effect between two superfluid time crystals S. Autti1;2∗, P.J. Heikkinen1;3, J.T. M¨akinen1;4;5, G.E. Volovik1;6, V.V. Zavjalov1;2, and V.B. Eltsov1y 1Low Temperature Laboratory, Department of Applied Physics, Aalto University, POB 15100, FI-00076 AALTO, Finland. yvladimir.eltsov@aalto.fi 2Department of Physics, Lancaster University, Lancaster LA1 4YB, UK. *[email protected] 3Department of Physics, Royal Holloway, University of London, Egham, Surrey, TW20 0EX, UK.
    [Show full text]
  • Lecture 10: Superconducting Devices Introduction
    Phys 769: Selected Topics in Condensed Matter Physics Summer 2010 Lecture 10: Superconducting devices Lecturer: Anthony J. Leggett TA: Bill Coish Introduction So far, we described only the superconducting ground state. Before proceeding to the main topic of this lecture, we need to say a little about the simplest excited states. For this purpose it is easier to use the original representation of BCS, in which the condition of particle number conservation is relaxed and the ground state has the form of a product of states referring to the occupation of the pair of states (k ↑, −k ↓): in obvious notation, 2 2 ΨBCS = Φk, Φk = uk |00i + vk |11i , |uk| + |vk| = 1 (1) Yk where |00i is the state in which neither k ↑ nor −k ↓ is occupied, |11i is that in which both are, and uk,vk are complex coefficients (though the usual convention is to take uk real). From the identification (lecture 9, Eq. (30)) of the Fourier-transformed wave function Fk with the “anomalous average” hN − 2| a−k↓ak↑ |Ni (which in the BCS representation becomes simply ha−k↓ak↑i we find ∗ Fk = ukvk. (2) In this representation we can associate a contribution to the kinetic and potential energy with each pair state (k ↑, −k ↓) separately (but must remember not to double-count). The contribution hV ik to the potential energy (excluding as usual the Hartree and Fock terms) is simply ∗ hV ik = −2∆kFk. (3) In the case of the kinetic energy, it is most convenient to calculate it relative to the value in the normal ground state (hnki = θ(kF − k)), which is 0 for ǫk > 0 and −2|ǫk| for ǫk < 0.
    [Show full text]
  • Mystery Solved of the Sawtooth Josephson Effect in Bismuth
    Journal Club for Condensed Matter Physics JCCM March 2018 01 http://www.condmatjclub.org Mystery solved of the sawtooth Josephson effect in bismuth 1. Ballistic edge states in bismuth nanowires revealed by SQUID interferometry Authors: A. Murani, A.Yu. Kasumov, S. Sengupta, Yu.A. Kasumov, V.T. Volkov, I.I. Khodos, F. Brisset, R. Delagrange, A. Chepelianskii, R. Deblock, H. Bouchiat, and S. Gu´eron Nature Communications 8, 15941 (2017) 2. Higher-order topology in bismuth Authors: F. Schindler, Z. Wang, M.G. Vergniory, A.M. Cook, A. Murani, S. Sengupta, A.Yu. Kasumov, R. Deblock, S. Jeon, I. Drozdov, H. Bouchiat, S. Gu´eron,A. Yazdani, B.A. Bernevig, and T. Neupert arXiv:1802.02585 Recommended with a Commentary by Carlo Beenakker, Instituut-Lorentz, Leiden University A challenging theoretical problem from the 1960's was to calculate the supercurrent through a clean Josephson junction of length L long compared to the superconducting co- herence length ξ. The calculation is complicated because every other energy level in the junction contributes with opposite sign to the supercurrent, and the resulting alternating series has to be summed with great accuracy to finally arrive at the correct answer: A piece- wise linear dependence of the supercurrent I on the phase difference φ, distinct from the sinusoidal dependence in a short junction. The linearity can be understood by noting that the regime L > ξ calls for a local relation between the current density and the gradient φ/L of the phase. Because I must be a 2π-periodic function of φ, the linear rise I / φ/L is interrupted by a jump when φ = ±π, resulting in a sawtooth current-phase relationship.
    [Show full text]
  • Quantum Oscillations Between Two Weakly Coupled Reservoirs Of
    letters to nature tions for the oscillations to exist in superfluids are that two samples of superfluid be separated by a region small enough so that the Quantum oscillations between wavefunctions of each part can weakly penetrate and overlap that of the other. An example of this would be two reservoirs of superfluid two weakly coupled helium in contact through a small aperture. Both the diameter and 3 the length of the aperture must be comparable to the superfluid reservoirs of superfluid He healing length7. This is the minimum length scale over which the magnitude of the superfluid wave function is allowed to vary for S. V. Pereverzev*, A. Loshak, S. Backhaus, J. C. Davis & R. E. Packard Physics Department, University of California, Berkeley, California 94720, USA ......................................................................................................................... Arguments first proposed over thirty years ago, based on funda- mental quantum-mechanical principles, led to the prediction1–3 that if macroscopic quantum systems are weakly coupled together, particle currents should oscillate between the two systems. The conditions for these quantum oscillations to occur are that the two systems must both have a well defined quantum phase, f, and a different average energy per particle, m: the term ‘weakly coupled’ means that the wavefunctions describing the systems must overlap slightly. The frequency of the resulting oscillations is then given by f =(m2−m1)/h, where h is Planck’s constant. To date, the only observed example of this phenomenon is the oscillation of electric current between two superconductors coupled by a Josephson tunnelling weak link4. Here we report the observation of oscillating mass currents between two reservoirs of superfluid 3He, the weak link being provided by an array of submicrometre apertures in a membrane separating the reservoirs.
    [Show full text]
  • Fractional Josephson Effect: a Missing Step Is a Key Step
    Fractional Josephson Effect: A Missing Step Is A Key Step Physicists are searching for superconducting materials that can host Majoranas. New evidence for these elusive particles is provided by missing Shapiro steps in a Josephson effect mediated by an accidental Dirac semimetal. Fan Zhang1* and Wei Pan2* 1Department of Physics, University of Texas at Dallas, Richardson, TX, USA. 2Sandia National LaBoratories, AlBuquerque, NM and Livermore, CA, USA. *e-mail: [email protected]; [email protected]. In a uniform superconductor, electrons form Cooper pairs that pick up the same quantum mechanical phase for their bosonic wavefunctions. This spontaneously breaks the gauge symmetry of electromagnetism. In 1962 Josephson predicted [1], and it was subsequently observed, that Cooper pairs can quantum mechanically tunnel between two weakly coupled superconductors that have a phase difference ϕ. The resulting supercurrent is a 2π periodic function of the phase difference ϕ across the junction. This is the celebrated Josephson effect. More recently, a fractional Josephson effect related to the presence of Majorana bound states – Majoranas – has been predicted for topological superconductors. This fractional Josephson effect has a characteristic 4π periodic current-phase relation. Now, writing in Nature Materials, Chuan Li and colleagues [2] report experiments that utilize nanoscale phase-sensitive junction technology to induce superconductivity in a fine-tuned Dirac semimetal Bi0.97Sb0.03 and discover a significant contribution of 4π periodic supercurrent in Nb-Bi0.97Sb0.03-Nb Josephson junctions under radio frequency irradiation. Strong motivation for this work is provided by the search for, and manipulation of, Majoranas that have been predicted to exist in topological superconductors [3-7].
    [Show full text]
  • Arxiv:1907.13284V1 [Cond-Mat.Other] 31 Jul 2019 Ative Charge Is Broken
    Theory of generalized Josephson effects Aron J. Beekman∗ Department of Physics, and Research and Education Center for Natural Sciences, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan (Dated: August 1, 2019) The DC Josephson effect is the flow of supercurrent across a weak link between two superconduc- tors with a different value of their order parameter, the phase. We generalize this notion to any kind of spontaneous continuous symmetry breaking. The quantity that flows between the two systems is identified as the Noether current associated with the broken symmetry. The AC Josephson effect is identified as the oscillations due to the energy difference between the two systems caused by an imposed asymmetric chemical potential. As an example of novel physics, a Josephson effect is pre- dicted between two crystalline solids, potentially measurable as a force periodic in the separation distance. The prediction by Josephson [1] of a DC current flow- (see Fig. 1). The only assumption is that the order pa- ing between two superconductors separated by a small rameters of the two systems couple to each other in a way distance, with zero voltage bias, revealed two important that favors a uniform configuration. This assumption is concepts. First, the order parameter can rightfully be very plausible if one considers the two systems as parts of regarded as a quantum field with an equation of motion, one large system that therefore prefers to break the sym- that does not vanish abruptly at the edge of a sample metry uniformly. Explicitly, the coupling Hamiltonian but must fall off in a continuous fashion.
    [Show full text]
  • Space- and Time-Crystallization Effects in Multicomponent Superfluids
    PHYSICAL REVIEW B 101, 020505(R) (2020) Rapid Communications Space- and time-crystallization effects in multicomponent superfluids Nikolay Prokof’ev Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA and National Research Center “Kurchatov Institute,” 123182 Moscow, Russia Boris Svistunov Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA; National Research Center “Kurchatov Institute,” 123182 Moscow, Russia; and Wilczek Quantum Center, School of Physics and Astronomy and T. D. Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China (Received 4 September 2019; revised manuscript received 20 December 2019; published 14 January 2020) We observe that space- and time-crystallization effects in multicomponent superfluids—while having the same physical origin and mathematical description as in the single-component case—are conceptually much more straightforward. Specifically, the values of the temporal and spatial periods are absolute rather than relative, and the broken translation symmetry in space and/or time can be revealed with experiments involving only one equilibrium sample. We discuss two realistic setups—one with cold atoms and another one with bilayer superconductors—for the observation of space and time crystallization in two-component counterflow superfluids. DOI: 10.1103/PhysRevB.101.020505 The superfluid long-range order—either genuine or, in superimposing two matter waves with opposite wave vectors lower dimensions, topological/algebraic—is associated with [3] nicely visualize the fact that superflows break translation the emergence of a well-defined (modulo 2π), defect-free symmetry and thus qualify to be called space crystals. Su- field of a coarse-grained phase, (r, t ); see, e.g., Ref. [1]. In percurrent states in three-dimensional superfluids do not form what follows, we discuss the genuine long-range order only.
    [Show full text]